PHP file not getting variable sent via AJAX using POST

I'm trying to send a jquery variable to a php script as part of a search feature I'm building for a website. I wish to use AJAX to perform the request for the php file and so far I've gotten this as my new-search.js script:

$('#bt_search').click(function(){
        $keyword = $('#keyword').val();//get the keyword from the input box
        $contentArray = []; //Hold checked "content" filters
        $typeArray = []; //Hold checked "type" filters
        $locationArray = []; //Hold checked "location" filters

        //Content Filter - cycle through each filter and add value of checked ones to array
        $('.content-filter :checked').each(function(){
            $contentArray.push(this.value);
        })

        //Type Filter
        $('.type-filter :checked').each(function(){
            $typeArray.push(this.value);
        })

        //Location Filter
        $('.location-filter :checked').each(function(){
            $locationArray.push(this.value);
        })

        //Testing 
        console.log("Keyword: " + $keyword);
        console.log("Content Filters: " + $contentArray);
        console.log("Type Filters: " + $typeArray);
        console.log("Location Filters: " + $locationArray);


        /*
         * Make AJAX Request to "new-search-get-results.php", passing 
         * keyword and filter arrays to the requested file.
         * 
         */ 
        $.ajax({
            url: "../pages/ajax/new-search-get-results.php",
            data: JSON.stringify({keyword: $keyword}),
            type: "POST",
            success: function(response){
                console.log(response);
            }
        });

The above is working, however I'm running into trouble with the response I get back from the new-search-get-results.php file. This is the error:

( ! ) Notice: Undefined index: keyword in C:\wamp\www\mysite.tld\pages\ajax\new-search-get-results.php on line 6

The line it relates to in the php file is: $keyword = $_POST['keyword'];

Does anyone know where I am going wrong so I can fix this error? This is my new-search-get-results.php file:

$keyword = $_POST['keyword'];
echo $keyword;